Bohr Model Electron Energy Levels?

I am about to graduate from high school and pursue my physics degree! Please help clear up these questions I have :)

Ok so I know about spectroscopy and how electromagnetic radiation causes electrons to gain more energy and move to a more excited state...emission absorption spectrums yada yada. I have a couple of questions however.

What makes an electron lose the energy it gains from the electromagnetic radiation? Why must it emit the photons and not simply just stay in the excited state? Is it an entropy problem or does it lose a certain amount of kinetic energy and the rest of the "gap" between energy levels is emitted out. That leads to my second question.

Do electrons emit the same radiation as it absorbed when it goes down the subsequent energy level? If so, doesn't that categorize it as a black-body?

Is thermodynamic entropy simply a mathematical problem...like statistical...or is there a physical reason for it? I apologize if that doesn't make much sense. In essence...why does entropy occur? I would assume it would just be math related to the statistics of a system...or maybe im totally off.

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